Chemistry 360 Spring 2015 Dr. Jean M. Standard April 22, 2015 Problem Set 13 Good review problems in Engel & Reid (3rd Ed.): 35.31, 35.32, 35.35, 35.36, 35.37, 35.40 1. "→ P follows second-order kinetics. The rate constant for the reaction is k=3.50×10–4 The reaction 2A " Lmol–1s–1. Determine the time required for the concentration of A to drop from its initial value of 0.260 mol/L to 0.011 mol/L. € 2. One of the hazards of nuclear explosions is the generation of 90Sr and its subsequent incorporation into the bones in place of calcium. Suppose 1 mg of 90Sr was absorbed into the body. How much will remain after 10 years, 20 years, and 50 years if none was lost metabolically? Note that 90Sr has a half-life of 28.1 years and that nuclear decay follows first-order kinetics. 3. "→ P follows second-order kinetics. Initially, the concentration of A was 0.075 mol/L. The reaction 2A " After 1 hour, the concentration had fallen to 0.020 mol/L. Determine the rate constant for the reaction and the half-life. € 4. k k –1 1 → B "" 2→ C A particular consecutive reaction, A "" , has rate constants given by k1 = 0.01s and k 2 = 0.001s –1 . Sketch a graph of [A], [B], and [C] as functions of time and calculate the time at which the intermediate B reaches its maximum concentration. € € € 5. The gas phase decomposition of acetic acid at high temperature (1189 K) proceeds by way of two parallel reactions, k CH 3COOH 1→ "" CH 3COOH 2 "" → k CH 4 + CO 2 k1 = 3.74 s –1 H 2C = C = O + H 2O k 2 = 4.65 s –1. Calculate the ratio of ketene (H2C=C=O) concentration to methane concentration and determine the maximum percent yield € of ketene (H2C=C=O). 2 6. For the reaction A + B C + D , various initial rate measurements were made starting with A and B only and then C and D only. From the data below, calculate the equilibrium constant for the reaction. [A]o [B]o Initial Rate (mol/L) (mol/L) (molL–1s–1) 0.660 1.23 1.081×10–5 4.01 1.23 6.577×10–5 4.01 2.25 6.568×10–5 [C]o [D]o Initial Rate (mol/L) (mol/L) (molL–1s–1) 2.88 0.995 7.805×10–7 2.88 1.65 1.290×10–6 1.01 1.65 1.300×10–6 7. The second-order rate constant for the decomposition of a certain substance is 1.70×10–2 Lmol–1s–1 at 30ºC and 2.01×10–2 Lmol–1s–1 at 37ºC. Determine the activation energy and pre-exponential factor. 8. Nitrous oxide, N2O, decomposes thermally at high temperatures. The measured rate constants for the gas phase decomposition of N2O at different temperatures [S. K. Ross et al., J. Phys. Chem. A 1997, 101, 1104] are given in the table below. T (K) k (cm3 molecule–1 s–1) 2056 6.79×10–16 2095 8.38×10–16 2132 1.03×10–15 2173 1.39×10–15 Assuming Arrhenius behavior, determine the activation energy (in kJ/mol) and the pre-exponential factor (in units of cm3 molecule–1 s–1). 9. Many reactions double their rates with a 10˚C rise in temperature. Assume that the rate of a reaction is measured at 305 and 315 K. What must the energy of activation be if the rate of reaction at 315 K is twice the rate of reaction at 305 K?